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@@ -1,31 +1,50 @@
-<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
- "http://www.w3.org/TR/html4/loose.dtd"&gt;
+<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"
+ "http://www.w3.org/TR/REC-html40/loose.dtd"&gt;
<html>
-<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
-<meta name="GENERATOR" content="TtH 3.68">
+<meta name="GENERATOR" content="TtH 3.85">
+<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<style type="text/css"> div.p { margin-top: 7pt;}</style>
<style type="text/css"><!--
td div.comp { margin-top: -0.6ex; margin-bottom: -1ex;}
td div.comb { margin-top: -0.6ex; margin-bottom: -.6ex;}
td div.hrcomp { line-height: 0.9; margin-top: -0.8ex; margin-bottom: -1ex;}
td div.norm {line-height:normal;}
+ pre
+ {
+ border: 1px solid gray;
+ padding-top: 1em;
+ padding-bottom: 1em;
+ padding-left: 1em;
+ padding-right: 1em;
+ background-color: #F1F5F9; /* light blue-gray */
+ }
span.roman {font-family: serif; font-style: normal; font-weight: normal;}
span.overacc2 {position: relative; left: .8em; top: -1.2ex;}
span.overacc1 {position: relative; left: .6em; top: -1.2ex;} --></style>
-
+
<title> Introduction to Maxima</title>
<h1 align="center">Introduction to Maxima </h1>
-<h3 align="center">Richard H. Rand<br />Dept. of Theoretical and Applied Mechanics, Cornell University
+<h3 align="center">Richard H. Rand<br />
+Dept. of Theoretical and Applied Mechanics, Cornell University
<a href="#tthFtNtAAB" name="tthFrefAAB"><sup>1</sup></a> </h3>
<h3 align="center"> </h3>
<div class="p"><!----></div>
-
+ Copyright (c) 1988-2010 Richard H. Rand.
+
+<div class="p"><!----></div>
+This document is free; you can redistribute it and/or modify it under
+the terms of the GNU General Public License as published by the Free
+Software Foundation. See the GNU General Public License for more
+details at http://www.gnu.org/copyleft/gpl.html
+
+<div class="p"><!----></div>
+
<h1>Contents </h1><a href="#tth_sEc1"
>1&nbsp; Introduction </a><br />
<a href="#tth_sEc2"
@@ -50,7 +69,7 @@
</a></h2>
<div class="p"><!----></div>
-To invoke Maxima in Linux, type
+To invoke Maxima in a console, type
<pre>
maxima&nbsp;&lt;enter&#62;
@@ -70,20 +89,22 @@
</pre>
<div class="p"><!----></div>
-The <tt>(%i1)</tt> is a "label". Each input or output line is labelled and can be referred to by its
-own label for the rest of the session. <tt>i</tt> labels denote your commands and <tt>o</tt> labels
-denote displays of the machine's response. <em>Never use variable names like <tt>%i1</tt> or <tt>
-%o5</tt>, as these will be confused with the lines so labeled</em>.
+The <tt>(%i1)</tt> is a "label". Each input or output line is
+labelled and can be referred to by its own label for the rest of the
+session. <tt>i</tt> labels denote your commands and <tt>o</tt> labels
+denote displays of the machine's response. <em>Never use variable
+ names like <tt>%i1</tt> or <tt>%o5</tt>, as these will be confused with
+ the lines so labeled</em>.
<div class="p"><!----></div>
-Maxima distinguishes lower and upper case.
-All built-in functions have names which are lowercase only
-(<tt>sin</tt>, <tt>cos</tt>, <tt>save</tt>, <tt>load</tt>, etc).
-Built-in constants have lowercase names (<tt>%e</tt>, <tt>%pi</tt>, <tt>inf</tt>, etc).
-If you type <tt>SIN(x)</tt> or <tt>Sin(x)</tt>,
-Maxima assumes you mean something other than the built-in <tt>sin</tt> function.
-User-defined functions and variables can have names which are lower or upper case or both.
-<tt>foo(XY)</tt>, <tt>Foo(Xy)</tt>, <tt>FOO(xy)</tt> are all different.
+Maxima distinguishes lower and upper case. All built-in functions
+have names which are lowercase only (<tt>sin</tt>, <tt>cos</tt>, <tt>save</tt>,
+<tt>load</tt>, etc). Built-in constants have lowercase names (<tt>%e</tt>,
+<tt>%pi</tt>, <tt>inf</tt>, etc). If you type <tt>SIN(x)</tt> or <tt>
+ Sin(x)</tt>, Maxima assumes you mean something other than the built-in
+<tt>sin</tt> function. User-defined functions and variables can have
+names which are lower or upper case or both. <tt>foo(XY)</tt>, <tt>
+ Foo(Xy)</tt>, <tt>FOO(xy)</tt> are all different.
<div class="p"><!----></div>
<h2><a name="tth_sEc2">
@@ -105,55 +126,63 @@
For example:
<pre>
-(%i1)&nbsp;sum&nbsp;(1/x^2,&nbsp;x,&nbsp;1,&nbsp;10000);
-
+(%i1)&nbsp;sum&nbsp;(1/x^2,&nbsp;x,&nbsp;1,&nbsp;100000)$
+^C
Maxima&nbsp;encountered&nbsp;a&nbsp;Lisp&nbsp;error:
-&nbsp;Console&nbsp;interrupt.
+&nbsp;Interactive&nbsp;interrupt&nbsp;at&nbsp;#x7FFFF74A43C3.
Automatically&nbsp;continuing.
-To&nbsp;reenable&nbsp;the&nbsp;Lisp&nbsp;debugger&nbsp;set&nbsp;*debugger-hook*&nbsp;to&nbsp;nil.
+To&nbsp;enable&nbsp;the&nbsp;Lisp&nbsp;debugger&nbsp;set&nbsp;*debugger-hook*&nbsp;to&nbsp;nil.
(%i2)
</pre>
<div class="p"><!----></div>
</li>
-<li> In order to tell Maxima that you have finished your command, use the semicolon (<tt>;</tt>),
-followed by a return. Note that the return key alone does not signal that you are done with your
-input.
+<li> In order to tell Maxima that you have finished your command, use
+ the semicolon (<tt>;</tt>), followed by a return. Note that the return
+ key alone does not signal that you are done with your input.
<div class="p"><!----></div>
</li>
-<li> An alternative input terminator to the semicolon (<tt>;</tt>) is the dollar sign (<tt>$</tt>),
-which, however, supresses the display of Maxima's computation. This is useful if you are computing
-some long intermediate result, and you don't want to waste time having it displayed on the screen.
+<li> An alternative input terminator to the semicolon (<tt>;</tt>) is
+ the dollar sign (<tt>$</tt>), which, however, supresses the display of
+ Maxima's computation. This is useful if you are computing some long
+ intermediate result, and you don't want to waste time having it
+ displayed on the screen.
<div class="p"><!----></div>
</li>
-<li> If you wish to repeat a command which you have already given, say on line <tt>(%i5)</tt>, you may
-do so without typing it over again by preceding its label with two single quotes (<tt>"</tt>), i.e., <tt>
-"%i5</tt>. (Note that simply inputing <tt>%i5</tt> will not do the job - try it.)
+<li> If you wish to repeat a command which you have already given,
+ say on line <tt>(%i5)</tt>, you may do so without typing it over again
+ by preceding its label with two single quotes (<tt>"</tt>), i.e., <tt>
+ "%i5</tt>. (Note that simply inputing <tt>%i5</tt> will not do the job
+ - try it.)
<div class="p"><!----></div>
</li>
-<li> If you want to refer to the immediately preceding result computed my Maxima, you can either
-use its <tt>o</tt> label, or you can use the special symbol percent (<tt>%</tt>).
+<li> If you want to refer to the immediately preceding result
+ computed by Maxima, you can either use its <tt>o</tt> label, or you can
+ use the special symbol percent (<tt>%</tt>).
<div class="p"><!----></div>
</li>
-<li> The standard quantities e (natural log base), i (square root of <font face="symbol">-</font
+<li> The standard quantities e (natural log base), i (square root
+ of <font face="symbol">-</font
>1) and <font face="symbol">p</font
->
-(3.14159<font face="symbol">¼</font
->) are respectively referred to as <tt>%e</tt>, <tt>%i</tt>,
-and <tt>%pi</tt>. Note that the use of <tt>%</tt> here as a prefix
-is completely unrelated to the use of <tt>%</tt> to refer to the preceding result computed.
+> (3.14159<font face="symbol">Â¼</font
+>) are respectively referred to as
+ <tt>%e</tt>, <tt>%i</tt>,
+ and <tt>%pi</tt>. Note that the use of <tt>%</tt> here as a prefix
+ is completely unrelated to the use of <tt>%</tt> to refer to the
+ preceding result computed.
<div class="p"><!----></div>
</li>
-<li> In order to assign a value to a variable, Maxima uses the colon (<tt>:</tt>), not the equal
-sign. The equal sign is used for representing equations.
+<li> In order to assign a value to a variable, Maxima uses the colon
+ (<tt>:</tt>), not the equal sign. The equal sign is used for
+ representing equations.
<div class="p"><!----></div>
</li>
</ol>
@@ -182,7 +211,7 @@
<dt><b><tt>sqrt(x)</tt></b></dt>
<dd> square root of <tt>x</tt>.</dd>
</dl>
-Maxima's output is characterized by exact (rational) arithmetic. E.g.,
+Maxima's output is characterized by exact (rational) arithmetic. For example,
<pre>
(%i1)&nbsp;1/100&nbsp;+&nbsp;1/101;
@@ -198,29 +227,32 @@
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;5
(%o2)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(sqrt(2)&nbsp;+&nbsp;1)
(%i3)&nbsp;expand&nbsp;(%);
-(%o3)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;29&nbsp;sqrt(2)&nbsp;+&nbsp;41
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;7/2
+(%o3)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;3&nbsp;2&nbsp;&nbsp;&nbsp;&nbsp;+&nbsp;5&nbsp;sqrt(2)&nbsp;+&nbsp;41
</pre>
-However, it is often useful to express a result in decimal notation. This may be accomplished by
-following the expression you want expanded by "<tt>,numer</tt>":
+However, it is often useful to express a result in decimal notation.
+This may be accomplished by following the expression you want expanded
+by "<tt>,numer</tt>":
<pre>
(%i4)&nbsp;%,&nbsp;numer;
-(%o4)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;82.01219330881976
+(%o4)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;82.01219330881977
</pre>
-Note the use here of <tt>%</tt>
-to refer to the previous result. In this version of Maxima, <tt>numer</tt> gives 16 significant
-figures, of which the last is often unreliable. However, Maxima can offer <em>arbitrarily high
-precision</em> by using the <tt>bfloat</tt> function:
+Note the use here of <tt>%</tt>
+to refer to the previous result. In this version of Maxima, <tt>
+ numer</tt> gives 16 significant figures, of which the last is often
+unreliable. However, Maxima can offer <em>arbitrarily high
+ precision</em> by using the <tt>bfloat</tt> function:
<pre>
(%i5)&nbsp;bfloat&nbsp;(%o3);
-(%o5)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;8.201219330881976B1
+(%o5)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;8.201219330881976b1
</pre>
-The number of significant figures displayed is controlled by the Maxima variable <tt>fpprec</tt>, which
-has the default value of 16:
+The number of significant figures displayed is controlled by the
+Maxima variable <tt>fpprec</tt>, which has the default value of 16:
<pre>
(%i6)&nbsp;fpprec;
@@ -233,17 +265,18 @@
(%i7)&nbsp;fpprec:&nbsp;100;
(%o7)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;100
(%i8)&nbsp;''%i5;
-(%o8)&nbsp;8.20121933088197564152489730020812442785204843859314941221#
-2371240173124187540110412666123849550160561B1
+(%o8)&nbsp;8.20121933088197564152489730020812442785204843859314941221\
+2371240173124187540110412666123849550160561b1
</pre>
-Note the use of two single quotes (<tt>"</tt>) in <tt>(%i8)</tt> to repeat command <tt>(%i5)</tt>. Maxima can
-handle very large numbers without approximation:
+Note the use of two single quotes (<tt>"</tt>) in <tt>(%i8)</tt> to repeat
+command <tt>(%i5)</tt>. Maxima can handle very large numbers without
+approximation:
<pre>
(%i9)&nbsp;100!;
-(%o9)&nbsp;9332621544394415268169923885626670049071596826438162146859#
-2963895217599993229915608941463976156518286253697920827223758251#
+(%o9)&nbsp;9332621544394415268169923885626670049071596826438162146859\
+2963895217599993229915608941463976156518286253697920827223758251\
185210916864000000000000000000000000
</pre>
@@ -254,8 +287,9 @@
</a></h2>
<div class="p"><!----></div>
-Maxima's importance as a computer tool to facilitate analytical calculations becomes more evident
-when we see how easily it does algebra for us. Here's an example in which a polynomial is expanded:
+Maxima's importance as a computer tool to facilitate analytical
+calculations becomes more evident when we see how easily it does
+algebra for us. Here's an example in which a polynomial is expanded:
<pre>
(%i1)&nbsp;(x&nbsp;+&nbsp;3*y&nbsp;+&nbsp;x^2*y)^3;
@@ -264,11 +298,12 @@
(%i2)&nbsp;expand&nbsp;(%);
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;6&nbsp;&nbsp;3&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;4&nbsp;&nbsp;3&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;2&nbsp;&nbsp;3&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;3&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;5&nbsp;&nbsp;2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;3&nbsp;&nbsp;2
(%o2)&nbsp;x&nbsp;&nbsp;y&nbsp;&nbsp;+&nbsp;9&nbsp;x&nbsp;&nbsp;y&nbsp;&nbsp;+&nbsp;27&nbsp;x&nbsp;&nbsp;y&nbsp;&nbsp;+&nbsp;27&nbsp;y&nbsp;&nbsp;+&nbsp;3&nbsp;x&nbsp;&nbsp;y&nbsp;&nbsp;+&nbsp;18&nbsp;x&nbsp;&nbsp;y
-&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;4&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;3
-&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;+&nbsp;27&nbsp;x&nbsp;y&nbsp;&nbsp;+&nbsp;3&nbsp;x&nbsp;&nbsp;y&nbsp;+&nbsp;9&nbsp;x&nbsp;&nbsp;y&nbsp;+&nbsp;x
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;4&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;3
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;+&nbsp;27&nbsp;x&nbsp;y&nbsp;&nbsp;+&nbsp;3&nbsp;x&nbsp;&nbsp;y&nbsp;+&nbsp;9&nbsp;x&nbsp;&nbsp;y&nbsp;+&nbsp;x
</pre>
-Now suppose we wanted to substitute <tt>5/z</tt> for <tt>x</tt> in the above expression:
+Now suppose we wanted to substitute <tt>5/z</tt> for <tt>x</tt> in the above
+expression:
<div class="p"><!----></div>
<table border="0"><tr><td></td><td><table border="0"><tr><td></td><td width="1000">
@@ -312,8 +347,9 @@
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;z
</pre>
-Maxima can obtain exact solutions to systems of nonlinear algebraic equations. In this example we
-<tt>solve</tt> three equations in the three unknowns <tt>a</tt>, <tt>b</tt>, <tt>c</tt>:
+Maxima can obtain exact solutions to systems of nonlinear algebraic
+equations. In this example we <tt>solve</tt> three equations in the
+three unknowns <tt>a</tt>, <tt>b</tt>, <tt>c</tt>:
<pre>
(%i6)&nbsp;a&nbsp;+&nbsp;b*c&nbsp;=&nbsp;1;
@@ -334,13 +370,15 @@
&nbsp;&nbsp;&nbsp;&nbsp;sqrt(79)&nbsp;%i&nbsp;-&nbsp;11&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;10
</pre>
-Note that the display consists of a "list", i.e., some expression contained between two brackets
-<tt>[ ... ]</tt>, which itself contains two lists. Each of the latter contain a distinct solution
-to the simultaneous equations.
+Note that the display consists of a "list", i.e., some expression
+contained between two brackets <tt>[ ... ]</tt>, which itself contains
+two lists. Each of the latter contain a distinct solution to the
+simultaneous equations.
<div class="p"><!----></div>
-Trigonometric identities are easy to manipulate in Maxima. The function <tt>trigexpand</tt> uses the
-sum-of-angles formulas to make the argument inside each trig function as simple as possible:
+Trigonometric identities are easy to manipulate in Maxima. The
+function <tt>trigexpand</tt> uses the sum-of-angles formulas to make the
+argument inside each trig function as simple as possible:
<pre>
(%i10)&nbsp;sin(u&nbsp;+&nbsp;v)&nbsp;*&nbsp;cos(u)^3;
@@ -351,8 +389,9 @@
(%o11)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;cos&nbsp;(u)&nbsp;(cos(u)&nbsp;sin(v)&nbsp;+&nbsp;sin(u)&nbsp;cos(v))
</pre>
-The function <tt>trigreduce</tt>, on the other hand, converts an expression into a form which is a sum
-of terms, each of which contains only a single <tt>sin</tt> or <tt>cos</tt>:
+The function <tt>trigreduce</tt>, on the other hand, converts an
+expression into a form which is a sum of terms, each of which contains
+only a single <tt>sin</tt> or <tt>cos</tt>:
<pre>
(%i12)&nbsp;trigreduce&nbsp;(%o10);
@@ -361,8 +400,8 @@
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;8&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;8
</pre>
-The functions <tt>realpart</tt> and <tt>imagpart</tt> will return the real and imaginary parts of a
-complex expression:
+The functions <tt>realpart</tt> and <tt>imagpart</tt> will return the real
+and imaginary parts of a complex expression:
<pre>
(%i13)&nbsp;w:&nbsp;3&nbsp;+&nbsp;k*%i;
@@ -382,8 +421,9 @@
</a></h2>
<div class="p"><!----></div>
-Maxima can compute derivatives and integrals, expand in Taylor series, take limits, and obtain exact
-solutions to ordinary differential equations. We begin by defining the symbol <tt>f</tt> to be the
+Maxima can compute derivatives and integrals, expand in Taylor series,
+take limits, and obtain exact solutions to ordinary differential
+equations. We begin by defining the symbol <tt>f</tt> to be the
following function of <tt>x</tt>:
<pre>
@@ -429,13 +469,14 @@
(%o4)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;1
(%i5)&nbsp;integrate&nbsp;(1/x,&nbsp;x,&nbsp;0,&nbsp;inf);
-Integral&nbsp;is&nbsp;divergent
-&nbsp;--&nbsp;an&nbsp;error.&nbsp;&nbsp;Quitting.&nbsp;&nbsp;To&nbsp;debug&nbsp;this&nbsp;try&nbsp;debugmode(true);
+defint:&nbsp;integral&nbsp;is&nbsp;divergent.
+&nbsp;--&nbsp;an&nbsp;error.&nbsp;To&nbsp;debug&nbsp;this&nbsp;try:&nbsp;debugmode(true);
</pre>
-Next we define the simbol <tt>g</tt> in terms of <tt>f</tt> (previously defined in <tt>%i1</tt>) and the
-hyperbolic sine function, and find its Taylor series expansion (up to, say, order 3 terms) about the
-point <tt>x = 0</tt>:
+Next we define the simbol <tt>g</tt> in terms of <tt>f</tt> (previously
+defined in <tt>%i1</tt>) and the hyperbolic sine function, and find its
+Taylor series expansion (up to, say, order 3 terms) about the point
+<tt>x = 0</tt>:
<div class="p"><!----></div>
<table border="0"><tr><td></td><td><table border="0"><tr><td></td><td width="1000">
@@ -467,7 +508,8 @@
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;k
</pre>
-Maxima also permits derivatives to be represented in unevaluated form (note the quote):
+Maxima also permits derivatives to be represented in unevaluated form
+(note the quote):
<pre>
(%i9)&nbsp;'diff&nbsp;(y,&nbsp;x);
@@ -476,8 +518,8 @@
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;dx
</pre>
-The quote operator in <tt>(%i9)</tt> means "do not evaluate". Without it, Maxima would have obtained
-0:
+The quote operator in <tt>(%i9)</tt> means "do not evaluate". Without
+it, Maxima would have obtained 0:
<pre>
(%i10)&nbsp;diff&nbsp;(y,&nbsp;x);
@@ -511,9 +553,10 @@
</a></h2>
<div class="p"><!----></div>
-Maxima can compute the determinant, inverse and eigenvalues and eigenvectors of matrices which have
-symbolic elements (i.e., elements which involve algebraic variables.) We begin by entering a matrix
-<tt>m</tt> element by element:
+Maxima can compute the determinant, inverse and eigenvalues and
+eigenvectors of matrices which have symbolic elements (i.e., elements
+which involve algebraic variables.) We begin by entering a matrix <tt>
+ m</tt> element by element:
<pre>
(%i1)&nbsp;m:&nbsp;entermatrix&nbsp;(3,&nbsp;3);
@@ -569,8 +612,9 @@
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;a&nbsp;+&nbsp;1
</pre>
-In <tt>(%i4)</tt>, the modifier <tt>detout</tt> keeps the determinant outside the inverse. As a check, we
-multiply <tt>m</tt> by its inverse (note the use of the period to represent matrix multiplication):
+In <tt>(%i4)</tt>, the modifier <tt>detout</tt> keeps the determinant
+outside the inverse. As a check, we multiply <tt>m</tt> by its inverse
+(note the use of the period to represent matrix multiplication):
<pre>
(%i5)&nbsp;m&nbsp;.&nbsp;%o4;
@@ -613,21 +657,22 @@
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;sqrt(4&nbsp;a&nbsp;+&nbsp;5)&nbsp;-&nbsp;1&nbsp;&nbsp;sqrt(4&nbsp;a&nbsp;+&nbsp;5)&nbsp;+&nbsp;1
(%o8)&nbsp;[[[-&nbsp;-----------------,&nbsp;-----------------,&nbsp;-&nbsp;1],&nbsp;
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;2
-&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;sqrt(4&nbsp;a&nbsp;+&nbsp;5)&nbsp;-&nbsp;1&nbsp;&nbsp;&nbsp;&nbsp;sqrt(4&nbsp;a&nbsp;+&nbsp;5)&nbsp;-&nbsp;1
-[1,&nbsp;1,&nbsp;1]],&nbsp;[1,&nbsp;-&nbsp;-----------------,&nbsp;-&nbsp;-----------------],&nbsp;
-&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;2&nbsp;a&nbsp;+&nbsp;2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;2&nbsp;a&nbsp;+&nbsp;2
-&nbsp;&nbsp;&nbsp;&nbsp;sqrt(4&nbsp;a&nbsp;+&nbsp;5)&nbsp;+&nbsp;1&nbsp;&nbsp;sqrt(4&nbsp;a&nbsp;+&nbsp;5)&nbsp;+&nbsp;1
-[1,&nbsp;-----------------,&nbsp;-----------------],&nbsp;[1,&nbsp;-&nbsp;1,&nbsp;0]]
-&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;2&nbsp;a&nbsp;+&nbsp;2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;2&nbsp;a&nbsp;+&nbsp;2
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;sqrt(4&nbsp;a&nbsp;+&nbsp;5)&nbsp;-&nbsp;1&nbsp;&nbsp;&nbsp;&nbsp;sqrt(4&nbsp;a&nbsp;+&nbsp;5)&nbsp;-&nbsp;1
+[1,&nbsp;1,&nbsp;1]],&nbsp;[[[1,&nbsp;-&nbsp;-----------------,&nbsp;-&nbsp;-----------------]],&nbsp;
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;2&nbsp;a&nbsp;+&nbsp;2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;2&nbsp;a&nbsp;+&nbsp;2
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;sqrt(4&nbsp;a&nbsp;+&nbsp;5)&nbsp;+&nbsp;1&nbsp;&nbsp;sqrt(4&nbsp;a&nbsp;+&nbsp;5)&nbsp;+&nbsp;1
+[[1,&nbsp;-----------------,&nbsp;-----------------]],&nbsp;[[1,&nbsp;-&nbsp;1,&nbsp;0]]]]
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;2&nbsp;a&nbsp;+&nbsp;2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;2&nbsp;a&nbsp;+&nbsp;2
</pre>
-In <tt>%o8</tt>, the first triple gives the eigenvalues of <tt>m</tt> and the next gives their respective
-multiplicities (here each is unrepeated). The next three triples give the corresponding
-eigenvectors of <tt>m</tt>. In order to extract from this expression one of these eigenvectors, we may
-use the <tt>part</tt> function:
+ In <tt>%o8</tt>, the first triple gives the eigenvalues of <tt>m</tt> and
+ the next gives their respective multiplicities (here each is
+ unrepeated). The next three triples give the corresponding
+ eigenvectors of <tt>m</tt>. In order to extract from this expression
+ one of these eigenvectors, we may use the <tt>part</tt> function:
<pre>
-(%i9)&nbsp;part&nbsp;(%,&nbsp;2);
+(%i9)&nbsp;part&nbsp;(%o23,&nbsp;2,&nbsp;1,&nbsp;1);
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;sqrt(4&nbsp;a&nbsp;+&nbsp;5)&nbsp;-&nbsp;1&nbsp;&nbsp;&nbsp;&nbsp;sqrt(4&nbsp;a&nbsp;+&nbsp;5)&nbsp;-&nbsp;1
(%o9)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[1,&nbsp;-&nbsp;-----------------,&nbsp;-&nbsp;-----------------]
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;2&nbsp;a&nbsp;+&nbsp;2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;2&nbsp;a&nbsp;+&nbsp;2
@@ -640,14 +685,17 @@
</a></h2>
<div class="p"><!----></div>
-So far, we have used Maxima in the interactive mode, rather like a calculator. However, for
-computations which involve a repetitive sequence of commands, it is better to execute a program.
-Here we present a short sample program to calculate the critical points of a function <tt>f</tt> of two
-variables <tt>x</tt> and <tt>y</tt>. The program cues the user to enter the function <tt>f</tt>, then it
-computes the partial derivatives <tt>f</tt><sub><tt>x</tt></sub> and <tt>f</tt><sub><tt>y</tt></sub>, and then it uses the Maxima
-command <tt>solve</tt> to obtain solutions to <tt>f</tt><sub><tt>x</tt></sub><tt> = </tt><tt>f</tt><sub><tt>y</tt></sub><tt> = </tt><tt>0</tt>. The program is written outside
-of Maxima with a text editor, and then loaded into Maxima with the <tt>batch</tt> command. Here is the
-program listing:
+So far, we have used Maxima in the interactive mode, rather like a
+calculator. However, for computations which involve a repetitive
+sequence of commands, it is better to execute a program. Here we
+present a short sample program to calculate the critical points of a
+function <tt>f</tt> of two variables <tt>x</tt> and <tt>y</tt>. The program
+cues the user to enter the function <tt>f</tt>, then it computes the
+partial derivatives <tt>f</tt><sub><tt>x</tt></sub> and <tt>f</tt><sub><tt>y</tt></sub>, and then it
+uses the Maxima command <tt>solve</tt> to obtain solutions to
+<tt>f</tt><sub><tt>x</tt></sub><tt> = </tt><tt>f</tt><sub><tt>y</tt></sub><tt> = </tt><tt>0</tt>. The program is written outside of Maxima
+with a text editor, and then loaded into Maxima with the <tt>batch</tt>
+command. Here is the program listing:
<pre>
/*&nbsp;--------------------------------------------------------------------------&nbsp;
@@ -683,10 +731,12 @@
)$
</pre>
-The program (which is actually a function with no argument) is called <tt>critpts</tt>. Each line is a
-valid Maxima command which could be executed from the keyboard, and which is separated by the next
-command by a comma. The partial derivatives are stored in a variable named <tt>eqs</tt>, and the
-unknowns are stored in <tt>unk</tt>. Here is a sample run:
+The program (which is actually a function with no argument) is called
+<tt>critpts</tt>. Each line is a valid Maxima command which could be
+executed from the keyboard, and which is separated by the next command
+by a comma. The partial derivatives are stored in a variable named
+<tt>eqs</tt>, and the unknowns are stored in <tt>unk</tt>. Here is a sample
+run:
<pre>&nbsp;
(%i1)&nbsp;batch&nbsp;("critpts.max");
@@ -702,14 +752,14 @@
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;2&nbsp;&nbsp;&nbsp;&nbsp;3
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;y&nbsp;&nbsp;+&nbsp;x
f&nbsp;=&nbsp;&nbsp;(y&nbsp;+&nbsp;x)&nbsp;%e&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-(%o3)&nbsp;[[x&nbsp;=&nbsp;0.4588955685487&nbsp;%i&nbsp;+&nbsp;0.35897908710869,&nbsp;
-y&nbsp;=&nbsp;0.49420173682751&nbsp;%i&nbsp;-&nbsp;0.12257873677837],&nbsp;
-[x&nbsp;=&nbsp;0.35897908710869&nbsp;-&nbsp;0.4588955685487&nbsp;%i,&nbsp;
-y&nbsp;=&nbsp;-&nbsp;0.49420173682751&nbsp;%i&nbsp;-&nbsp;0.12257873677837],&nbsp;
-[x&nbsp;=&nbsp;0.41875423272348&nbsp;%i&nbsp;-&nbsp;0.69231242044203,&nbsp;
-y&nbsp;=&nbsp;0.4559120701117&nbsp;-&nbsp;0.86972626928141&nbsp;%i],&nbsp;
-[x&nbsp;=&nbsp;-&nbsp;0.41875423272348&nbsp;%i&nbsp;-&nbsp;0.69231242044203,&nbsp;
-y&nbsp;=&nbsp;0.86972626928141&nbsp;%i&nbsp;+&nbsp;0.4559120701117]]
+(%o3)&nbsp;[[x&nbsp;=&nbsp;.4588955685487001&nbsp;%i&nbsp;+&nbsp;.3589790871086935,&nbsp;
+y&nbsp;=&nbsp;.4942017368275118&nbsp;%i&nbsp;-&nbsp;.1225787367783657],&nbsp;
+[x&nbsp;=&nbsp;.3589790871086935&nbsp;-&nbsp;.4588955685487001&nbsp;%i,&nbsp;
+y&nbsp;=&nbsp;-&nbsp;.4942017368275118&nbsp;%i&nbsp;-&nbsp;.1225787367783657],&nbsp;
+[x&nbsp;=&nbsp;.4187542327234816&nbsp;%i&nbsp;-&nbsp;.6923124204420268,&nbsp;
+y&nbsp;=&nbsp;0.455912070111699&nbsp;-&nbsp;.8697262692814121&nbsp;%i],&nbsp;
+[x&nbsp;=&nbsp;-&nbsp;.4187542327234816&nbsp;%i&nbsp;-&nbsp;.6923124204420268,&nbsp;
+y&nbsp;=&nbsp;.8697262692814121&nbsp;%i&nbsp;+&nbsp;0.455912070111699]]
</pre>
@@ -718,168 +768,198 @@
8</a>&nbsp;&nbsp;A partial list of Maxima functions</h2>
<div class="p"><!----></div>
-See the Maxima reference manual <tt>doc/html/maxima_toc.html</tt> (under the main Maxima installation directory).
-From Maxima itself, you can use <tt>describe(<i>function name</i>)</tt>.
+See the Maxima reference manual <tt>doc/html/maxima_toc.html</tt> (under
+the main Maxima installation directory). From Maxima itself, you can
+use <tt>describe(<i>function name</i>)</tt>.
<div class="p"><!----></div>
<dl compact="compact">
<dt><b><tt>allroots(a)</tt></b></dt>
- <dd> Finds all the (generally complex) roots of the polynomial equation <tt>
- A</tt>, and lists them in <tt>numer</tt>ical format (i.e. to 16 significant figures).</dd>
+ <dd> Finds all the (generally complex) roots of
+ the polynomial equation <tt>A</tt>, and lists them in <tt>numer</tt>ical
+ format (i.e. to 16 significant figures).</dd>
<dt><b><tt>append(a,b)</tt></b></dt>
- <dd> Appends the list <tt>b</tt> to the list <tt>a</tt>, resulting in a single
- list.</dd>
+ <dd> Appends the list <tt>b</tt> to the list <tt>a</tt>,
+ resulting in a single list.</dd>
<dt><b><tt>batch(a)</tt></b></dt>
<dd> Loads and runs a program with filename <tt>a</tt>.</dd>
<dt><b><tt>coeff(a,b,c)</tt></b></dt>
- <dd> Gives the coefficient of <tt>b</tt> raised to the power <tt>c</tt> in
- expression <tt>a</tt>.</dd>
+ <dd> Gives the coefficient of <tt>b</tt> raised to
+ the power <tt>c</tt> in expression <tt>a</tt>.</dd>
<dt><b><tt>concat(a,b)</tt></b></dt>
<dd> Creates the symbol <tt>ab</tt>.</dd>
<dt><b><tt>cons(a,b)</tt></b></dt>
<dd> Adds <tt>a</tt> to the list <tt>b</tt> as its first element.</dd>
<dt><b><tt>demoivre(a)</tt></b></dt>
- <dd> Transforms all complex exponentials in <tt>a</tt> to their trigonometric
- equivalents.</dd>
+ <dd> Transforms all complex exponentials in <tt>
+ a</tt> to their trigonometric equivalents.</dd>
<dt><b><tt>denom(a)</tt></b></dt>
<dd> Gives the denominator of <tt>a</tt>.</dd>
<dt><b><tt>depends(a,b)</tt></b></dt>
- <dd> Declares <tt>a</tt> to be a function of <tt>b</tt>. This is useful for
- writing unevaluated derivatives, as in specifying differential equations.</dd>
+ <dd> Declares <tt>a</tt> to be a function of <tt>
+ b</tt>. This is useful for writing unevaluated derivatives, as in
+ specifying differential equations.</dd>
<dt><b><tt>desolve(a,b)</tt></b></dt>
- <dd> Attempts to solve a linear system <tt>a</tt> of ODE's for unknowns <tt>b</tt>
- using Laplace transforms.</dd>
+ <dd> Attempts to solve a linear system <tt>a</tt> of
+ ODE's for unknowns <tt>b</tt> using Laplace transforms.</dd>
<dt><b><tt>determinant(a)</tt></b></dt>
- <dd> Returns the determinant of the square matrix <tt>a</tt>.</dd>
+ <dd> Returns the determinant of the square
+ matrix <tt>a</tt>.</dd>
<dt><b><tt>diff(a,b1,c1,b2,c2,...,bn,cn)</tt></b></dt>
- <dd> Gives the mixed partial derivative of <tt>a</tt> with
- respect to each <tt>bi</tt>, <tt>ci</tt> times. For brevity, <tt>diff(a,b,1)</tt> may be represented by
- <tt>diff(a,b)</tt>. <tt>'diff(...)</tt> represents the unevaluated derivative, useful in specifying
- a differential equation.</dd>
+ <dd> Gives the mixed partial
+ derivative of <tt>a</tt> with respect to each <tt>bi</tt>, <tt>ci</tt> times.
+ For brevity, <tt>diff(a,b,1)</tt> may be represented by <tt>
+ diff(a,b)</tt>. <tt>'diff(...)</tt> represents the unevaluated
+ derivative, useful in specifying a differential equation.</dd>
<dt><b><tt>eigenvalues(a)</tt></b></dt>
- <dd> Returns two lists, the first being the eigenvalues of the square
- matrix <tt>a</tt>, and the second being their respective multiplicities.</dd>
+ <dd> Returns two lists, the first being the
+ eigenvalues of the square matrix <tt>a</tt>, and the second being their
+ respective multiplicities.</dd>
<dt><b><tt>eigenvectors(a)</tt></b></dt>
- <dd> Does everything that <tt>eigenvalues</tt> does, and adds a list of the
- eigenvectors of <tt>a</tt>.</dd>
+ <dd> Does everything that <tt>eigenvalues</tt>
+ does, and adds a list of the eigenvectors of <tt>a</tt>.</dd>
<dt><b><tt>entermatrix(a,b)</tt></b></dt>
- <dd> Cues the user to enter an <tt>a</tt> &times;&nbsp;<tt>b</tt> matrix,
- element by element.</dd>
+ <dd> Cues the user to enter an <tt>a</tt> &times;&nbsp;<tt>b</tt> matrix, element by element.</dd>
<dt><b><tt>ev(a,b1,b2,...,bn)</tt></b></dt>
- <dd> Evaluates <tt>a</tt> subject to the conditions <tt>bi</tt>. In
- particular the <tt>bi</tt> may be equations, lists of equations (such as that returned by <tt>
- solve</tt>), or assignments, in which cases <tt>ev</tt> "plugs" the <tt>bi</tt> into <tt>a</tt>. The <tt>
- Bi</tt> may also be words such as <tt>numer</tt> (in which case the result is returned in numerical
- format), <tt>detout</tt> (in which case any matrix inverses in <tt>a</tt> are performed with the
- determinant factored out), or <tt>diff</tt> (in which case all differentiations in <tt>a</tt> are
- evaluated, i.e., <tt>'diff</tt> in <tt>a</tt> is replaced by <tt>diff</tt>). For brevity in a manual
- command (i.e., not inside a user-defined function), the <tt>ev</tt> may be dropped, shortening the
- syntax to <tt>a,b1,b2,...,bn</tt>.</dd>
+ <dd> Evaluates <tt>a</tt> subject to the
+ conditions <tt>bi</tt>. In particular the <tt>bi</tt> may be equations,
+ lists of equations (such as that returned by <tt>solve</tt>), or
+ assignments, in which cases <tt>ev</tt> "plugs" the <tt>bi</tt> into
+ <tt>a</tt>. The <tt>Bi</tt> may also be words such as <tt>numer</tt> (in
+ which case the result is returned in numerical format), <tt>detout</tt>
+ (in which case any matrix inverses in <tt>a</tt> are performed with the
+ determinant factored out), or <tt>diff</tt> (in which case all
+ differentiations in <tt>a</tt> are evaluated, i.e., <tt>'diff</tt> in <tt>
+ a</tt> is replaced by <tt>diff</tt>). For brevity in a manual command
+ (i.e., not inside a user-defined function), the <tt>ev</tt> may be
+ dropped, shortening the syntax to <tt>a,b1,b2,...,bn</tt>.</dd>
<dt><b><tt>expand(a)</tt></b></dt>
- <dd> Algebraically expands <tt>a</tt>. In particular multiplication is
- distributed over addition.</dd>
+ <dd> Algebraically expands <tt>a</tt>. In particular
+ multiplication is distributed over addition.</dd>
<dt><b><tt>exponentialize(a)</tt></b></dt>
- <dd> Transforms all trigonometric functions in <tt>a</tt> to their complex
- exponential equivalents.</dd>
+ <dd> Transforms all trigonometric functions
+ in <tt>a</tt> to their complex exponential equivalents.</dd>
<dt><b><tt>factor(a)</tt></b></dt>
<dd> Factors <tt>a</tt>.</dd>
<dt><b><tt>freeof(a,b)</tt></b></dt>
- <dd> Is true if the variable <tt>a</tt> is not part of the expression <tt>b</tt>.</dd>
+ <dd> Is true if the variable <tt>a</tt> is not part
+ of the expression <tt>b</tt>.</dd>
<dt><b><tt>grind(a)</tt></b></dt>
- <dd> Displays a variable or function <tt>a</tt> in a compact format. When used
- with <tt>writefile</tt> and an editor outside of Maxima, it offers a scheme for producing <tt>
- batch</tt> files which include Maxima-generated expressions.</dd>
+ <dd> Displays a variable or function <tt>a</tt> in a
+ compact format. When used with <tt>writefile</tt> and an editor
+ outside of Maxima, it offers a scheme for producing <tt>batch</tt>
+ files which include Maxima-generated expressions.</dd>
<dt><b><tt>ident(a)</tt></b></dt>
- <dd> Returns an <tt>a</tt> &times;&nbsp;<tt>a</tt> identity matrix.</dd>
+ <dd> Returns an <tt>a</tt> &times;&nbsp;<tt>a</tt>
+ identity matrix.</dd>
<dt><b><tt>imagpart(a)</tt></b></dt>
<dd> Returns the imaginary part of <tt>a</tt>.</dd>
<dt><b><tt>integrate(a,b)</tt></b></dt>
- <dd> Attempts to find the indefinite integral of <tt>a</tt> with respect to
- <tt>b</tt>.</dd>
+ <dd> Attempts to find the indefinite integral
+ of <tt>a</tt> with respect to <tt>b</tt>.</dd>
<dt><b><tt>integrate(a,b,c,d)</tt></b></dt>
- <dd> Attempts to find the indefinite integral of <tt>a</tt> with respect to
- <tt>b</tt>. taken from <tt>b</tt><tt>=</tt><tt>c</tt> to <tt>b</tt><tt>=</tt><tt>d</tt>. The limits of integration <tt>c</tt> and <tt>
- D</tt> may be taken is <tt>inf</tt> (positive infinity) of <tt>minf</tt> (negative infinity).</dd>
+ <dd> Attempts to find the indefinite
+ integral of <tt>a</tt> with respect to <tt>b</tt>. taken from
+ <tt>b</tt><tt>=</tt><tt>c</tt> to <tt>b</tt><tt>=</tt><tt>d</tt>. The limits of integration <tt>c</tt>
+ and <tt>d</tt> may be taken is <tt>inf</tt> (positive infinity) of <tt>
+ minf</tt> (negative infinity).</dd>
<dt><b><tt>invert(a)</tt></b></dt>
- <dd> Computes the inverse of the square matrix <tt>a</tt>.</dd>
+ <dd> Computes the inverse of the square matrix <tt>
+ a</tt>.</dd>
<dt><b><tt>kill(a)</tt></b></dt>
- <dd> Removes the variable <tt>a</tt> with all its assignments and properties from
- the current Maxima environment.</dd>
+ <dd> Removes the variable <tt>a</tt> with all its
+ assignments and properties from the current Maxima environment.</dd>
<dt><b><tt>limit(a,b,c)</tt></b></dt>
- <dd> Gives the limit of expression <tt>a</tt> as variable <tt>b</tt> approaches
- the value <tt>c</tt>. The latter may be taken as <tt>inf</tt> of <tt>minf</tt> as in <tt>integrate</tt>.</dd>
+ <dd> Gives the limit of expression <tt>a</tt> as
+ variable <tt>b</tt> approaches the value <tt>c</tt>. The latter may be
+ taken as <tt>inf</tt> of <tt>minf</tt> as in <tt>integrate</tt>.</dd>
<dt><b><tt>lhs(a)</tt></b></dt>
<dd> Gives the left-hand side of the equation <tt>a</tt>.</dd>
<dt><b><tt>loadfile(a)</tt></b></dt>
- <dd> Loads a disk file with filename <tt>a</tt> from the current default
- directory. The disk file must be in the proper format (i.e. created by a <tt>save</tt> command).</dd>
+ <dd> Loads a disk file with filename <tt>a</tt> from
+ the current default directory. The disk file must be in the proper
+ format (i.e. created by a <tt>save</tt> command).</dd>
<dt><b><tt>makelist(a,b,c,d)</tt></b></dt>
- <dd> Creates a list of <tt>a</tt>'s (each of which presumably depends on
- <tt>b</tt>), concatenated from <tt>b</tt><tt>=</tt><tt>c</tt> to <tt>b</tt><tt>=</tt><tt>d</tt></dd>
+ <dd> Creates a list of <tt>a</tt>'s (each of
+ which presumably depends on <tt>b</tt>), concatenated from
+ <tt>b</tt><tt>=</tt><tt>c</tt> to <tt>b</tt><tt>=</tt><tt>d</tt></dd>
<dt><b><tt>map(a,b)</tt></b></dt>
- <dd> Maps the function <tt>a</tt> onto the subexpressions of <tt>b</tt>.</dd>
+ <dd> Maps the function <tt>a</tt> onto the
+ subexpressions of <tt>b</tt>.</dd>
<dt><b><tt>matrix(a1,a2,...,an)</tt></b></dt>
<dd> Creates a matrix consisting of the rows <tt>ai</tt>, where each
- row <tt>ai</tt> is a list of <tt>m</tt> elements, <tt>[b1, b2, ..., bm]</tt>.</dd>
+ row <tt>ai</tt> is a list of <tt>m</tt> elements, <tt>[b1, b2, ..., bm]</tt>.</dd>
<dt><b><tt>num(a)</tt></b></dt>
<dd> Gives the numerator of <tt>a</tt>.</dd>
<dt><b><tt>ode2(a,b,c)</tt></b></dt>
- <dd> Attempts to solve the first- or second-order ordinary differential
- equation <tt>a</tt> for <tt>b</tt> as a function of <tt>c</tt>.</dd>
+ <dd> Attempts to solve the first- or second-order
+ ordinary differential equation <tt>a</tt> for <tt>b</tt> as a function of
+ <tt>c</tt>.</dd>
<dt><b><tt>part(a,b1,b2,...,bn)</tt></b></dt>
- <dd> First takes the <tt>b1</tt>th part of <tt>a</tt>, then the <tt>
- B2</tt>th part of that, and so on.</dd>
+ <dd> First takes the <tt>b1</tt>th part
+ of <tt>a</tt>, then the <tt>b2</tt>th part of that, and so on.</dd>
<dt><b><tt>playback(a)</tt></b></dt>
- <dd> Displays the last <tt>a</tt> (an integer) labels and their associated
- expressions. If <tt>a</tt> is omitted, all lines are played back. See the Manual for other
- options.</dd>
+ <dd> Displays the last <tt>a</tt> (an integer)
+ labels and their associated expressions. If <tt>a</tt> is omitted,
+ all lines are played back. See the Manual for other options.</dd>
<dt><b><tt>ratsimp(a)</tt></b></dt>
- <dd> Simplifies <tt>a</tt> and returns a quotient of two polynomials.</dd>
+ <dd> Simplifies <tt>a</tt> and returns a quotient of
+ two polynomials.</dd>
<dt><b><tt>realpart(a)</tt></b></dt>
<dd> Returns the real part of <tt>a</tt>.</dd>
<dt><b><tt>rhs(a)</tt></b></dt>
<dd> Gives the right-hand side of the equation <tt>a</tt>.</dd>
<dt><b><tt>save(a,b1,b2,..., bn)</tt></b></dt>
- <dd> Creates a disk file with filename <tt>a</tt> in the current
- default directory, of variables, functions, or arrays <tt>bi</tt>. The format of the file permits
- it to be reloaded into Maxima using the <tt>loadfile</tt> command. Everything (including labels)
- may be <tt>save</tt>d by taking <tt>b1</tt> equal to <tt>all</tt>.</dd>
+ <dd> Creates a disk file with
+ filename <tt>a</tt> in the current default directory, of variables,
+ functions, or arrays <tt>bi</tt>. The format of the file permits it to
+ be reloaded into Maxima using the <tt>loadfile</tt> command.
+ Everything (including labels) may be <tt>save</tt>d by taking <tt>b1</tt>
+ equal to <tt>all</tt>.</dd>
<dt><b><tt>solve(a,b)</tt></b></dt>
- <dd> Attempts to solve the algebraic equation <tt>a</tt> for the unknown <tt>b</tt>. A
- list of solution equations is returned. For brevity, if <tt>a</tt> is an equation of the form
- <tt>c</tt><tt> = </tt><tt>0</tt>, it may be abbreviated simply by the expression <tt>c</tt>.</dd>
+ <dd> Attempts to solve the algebraic equation <tt>
+ a</tt> for the unknown <tt>b</tt>. A list of solution equations is
+ returned. For brevity, if <tt>a</tt> is an equation of the form
+ <tt>c</tt><tt> = </tt><tt>0</tt>, it may be abbreviated simply by the expression
+ <tt>c</tt>.</dd>
<dt><b><tt>string(a)</tt></b></dt>
- <dd> Converts <tt>a</tt> to Maxima's linear notation (similar to Fortran's) just as if
- it had been typed in and puts <tt>a</tt> into the
- buffer for possible editing. The <tt>string</tt>'ed expression should not be used in a computation.</dd>
+ <dd> Converts <tt>a</tt> to Maxima's linear notation
+ (similar to Fortran's) just as if it had been typed in and puts <tt>
+ a</tt> into the buffer for possible editing. The <tt>string</tt>'ed
+ expression should not be used in a computation.</dd>
<dt><b><tt>stringout(a,b1,b2,...,bn)</tt></b></dt>
- <dd> Creates a disk file with filename <tt>a</tt> in the current
- default directory, of variables (e.g. labels) <tt>bi</tt>. The file is in a text format and is not
- reloadable into Maxima. However the strungout expressions can be incorporated into a Fortran,
- Basic or C program with a minimum of editing.</dd>
+ <dd> Creates a disk file with
+ filename <tt>a</tt> in the current default directory, of variables
+ (e.g. labels) <tt>bi</tt>. The file is in a text format and is not
+ reloadable into Maxima. However the strungout expressions can be
+ incorporated into a Fortran, Basic or C program with a minimum of
+ editing.</dd>
<dt><b><tt>subst(a,b,c)</tt></b></dt>
<dd> Substitutes <tt>a</tt> for <tt>b</tt> in <tt>c</tt>.</dd>
<dt><b><tt>taylor(a,b,c,d)</tt></b></dt>
- <dd> Expands <tt>a</tt> in a Taylor series in <tt>b</tt> about <tt>b</tt><tt>=</tt><tt>c</tt>,
- up to and including the term <tt>(</tt><tt>b</tt><font face="symbol">-</font
+ <dd> Expands <tt>a</tt> in a Taylor series in
+ <tt>b</tt> about <tt>b</tt><tt>=</tt><tt>c</tt>, up to and including the term
+ <tt>(</tt><tt>b</tt><font face="symbol">-</font
><tt>c</tt><tt>)</tt><sup><tt>d</tt></sup>. Maxima also supports Taylor expansions in more
- than one independent variable; see the Manual for details.</dd>
+ than one independent variable; see the Manual for details.</dd>
<dt><b><tt>transpose(a)</tt></b></dt>
<dd> Gives the transpose of the matrix <tt>a</tt>.</dd>
<dt><b><tt>trigexpand(a)</tt></b></dt>
- <dd> Is a trig simplification function which uses the sum-of-angles
- formulas to simplify the arguments of individual <tt>sin</tt>'s or <tt>cos</tt>'s. For example,
- <tt>trigexpand(sin(x+y))</tt> gives <tt>cos(x) sin(y) + sin(x) cos(y)</tt>.</dd>
+ <dd> Is a trig simplification function which
+ uses the sum-of-angles formulas to simplify the arguments of
+ individual <tt>sin</tt>'s or <tt>cos</tt>'s. For example, <tt>
+ trigexpand(sin(x+y))</tt> gives <tt>cos(x) sin(y) + sin(x) cos(y)</tt>.</dd>
<dt><b><tt>trigreduce(a)</tt></b></dt>
- <dd> Is a trig simplification function which uses trig identities to
- convert products and powers of <tt>sin</tt> and <tt>cos</tt> into a sum of terms, each of which
- contains only a single <tt>sin</tt> or <tt>cos</tt>. For example, <tt>trigreduce(sin(x)^2)</tt> gives
- <tt>(1 - cos(2x))/2</tt>.</dd>
+ <dd> Is a trig simplification function which
+ uses trig identities to convert products and powers of <tt>sin</tt> and
+ <tt>cos</tt> into a sum of terms, each of which contains only a single
+ <tt>sin</tt> or <tt>cos</tt>. For example, <tt>trigreduce(sin(x)^2)</tt>
+ gives <tt>(1 - cos(2x))/2</tt>.</dd>
<dt><b><tt>trigsimp(a)</tt></b></dt>
- <dd> Is a trig simplification function which replaces <tt>tan</tt>, <tt>sec</tt>,
- etc., by their <tt>sin</tt> and <tt>cos</tt> equivalents. It also uses the identity
- <tt>sin</tt><tt>(</tt><tt>)</tt><sup><tt>2</tt></sup> <tt>+</tt> <tt>cos</tt><tt>(</tt><tt>)</tt><sup><tt>2</tt></sup><tt> = </tt><tt>1</tt>.</dd>
+ <dd> Is a trig simplification function which
+ replaces <tt>tan</tt>, <tt>sec</tt>, etc., by their <tt>sin</tt> and <tt>
+ cos</tt> equivalents. It also uses the identity <tt>sin</tt><tt>(</tt><tt>)</tt><sup><tt>2</tt></sup> <tt>+</tt> <tt>cos</tt><tt>(</tt><tt>)</tt><sup><tt>2</tt></sup><tt> = </tt><tt>1</tt>.</dd>
</dl>
<div class="p"><!----></div>
@@ -889,11 +969,11 @@
<a name="tthFtNtAAB"></a><a href="#tthFrefAAB"><sup>1</sup></a>Adapted from "Perturbation Methods, Bifurcation Theory and Computer Algebra"
by Rand and Armbruster, Springer, 1987.
Adapted to <span class="roman">L</span><sup><span class="roman">A</span></sup><span class="roman">T</span><sub><span class="roman">E</span></sub><span class="roman">X</span>&nbsp;and HTML by Nelson L. Dias (nldias@...),
-SIMEPAR Technological Institute and Federal University of Paraná, Brazil.
+SIMEPAR Technological Institute and Federal University of ParanÃ¡, Brazil.
Updated by Robert Dodier, August 2005.
<br /><br /><hr /><small>File translated from
T<sub><font size="-1">E</font></sub>X
by <a href="http://hutchinson.belmont.ma.us/tth/"&gt;
T<sub><font size="-1">T</font></sub>H</a>,
-version 3.68.<br />On 21 Aug 2005, 12:26.</small>
+version 3.85.<br />On 26 Apr 2010, 00:45.</small>
</html>

Update of /cvsroot/maxima/site-xml
In directory sfp-cvsdas-4.v30.ch3.sourceforge.com:/tmp/cvs-serv14171
Modified Files:
download.xml
Log Message:
Information for Slackware users from Viktor T. Toth
Index: download.xml
===================================================================
RCS file: /cvsroot/maxima/site-xml/download.xml,v
retrieving revision 1.7
retrieving revision 1.8
diff -u -d -r1.7 -r1.8
--- download.xml 19 Mar 2009 00:45:45 -0000 1.7
+++ download.xml 19 Apr 2010 20:29:17 -0000 1.8
@@ -22,12 +22,20 @@
<h3>Linux</h3>
+<h4>Slackware</h4>
+
+<p>For Slackware users, an installation kit is provided as <kbd>maxima-x.y.z-i486-n_slack12.1.tgz</kbd>. This file can be installed using the <kbd>installpkg</kbd> command on most recent (version 12.0 and up) Slackware systems. The package includes binaries for four Lisps (CLISP, GCL, CMUCL, and SBCL) though you may find that âout of the boxâ, only the CLISP binary will function, as CLISP is included with Slackware distributions. Before you can run the other binaries, it may be necessary to download and install the appropriate Lisp.</p>
+
+<h4>RPM</h4>
+
<p>For an installation from RPM, you want at least two files: (1) <kbd>maxima-x.y.z-n.i386.rpm</kbd>, which contains scripts and documents, and (2) <kbd>maxima-exec-&lt;<var>lisp&#x00a0;version</var>>-x.y.z-n.i386.rpm</kbd>, which contains an executable Lisp image. You may also want (3) <kbd>maxima-xmaxima-x.y.z-n.i386.rpm</kbd>, the Xmaxima graphical user interface, but it is optional.</p>
<p>The maxima and maxima-exec RPMs depend on each other. Specify both in the rpm command:</p>
<pre>rpm -ivh maxima-x.y.z-n.i386.rpm maxima-exec-&lt;<var>lisp version</var>>-x.y.z-n.i386.rpm</pre>
+<h4>Source Code</h4>
+
<p>For an installation from source code, you want <kbd>maxima-x.y.z.tar.gz</kbd> or <kbd>maxima-x.y.z-n.src.rpm</kbd>. But you knew that.</p>
<p>Here are some notes that might be helpful. <a href="http://maxima.cvs.sourceforge.net/maxima/maxima/README.lisps?view=markup">README.lisps</a&gt; tells something about Lisp implementations, and <a href="http://maxima.cvs.sourceforge.net/maxima/maxima/README.rpms?view=markup">README.rpms</a&gt; tells something about RPM's.</p>

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